Additive Representation of Non-Additive Measures and the Choquet Integral

Itzhak Gilboa and David Schmeidler

No 985, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: This paper studies some new properties of set functions (and, in particular, "non-additive probabilities" or "capacities") and the Choquet integral with respect to such functions, in the case of a finite domain. We use an isomorphism between non-additive measures on the original space (of states of the world) and additive ones on a large space (of events), and embed the space of real-valued functions on the former in the corresponding space on the latter. This embedding gives rise to the following results: the Choquet integral with respect to any totally monotone capacity is an average over minima of the inegrand; the Choquet integral with respect to any capacity is the differences between minima of regular integrals over sets of additive measures; under fairly general conditions one may define a "Radon-Nikodym derivative" of one capacity with respect to another; the "optimistic" pseudo-Bayesian update of a non-additive measure follows from the Bayesian update of the corresponding additive measure on the large space. We also discuss the interpretation o these results and the new light they shed on the theory of expected utility maximization with respect to non-additive measures.

Date: 1992-04
References: Add references at CitEc
Citations: View citations in EconPapers (10)

Downloads: (external link)
http://www.kellogg.northwestern.edu/research/math/papers/985.pdf main text (application/pdf)

Related works:
Working Paper: Additive Representations of Non-Additive Measures and the Choquet Integral (1994)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nwu:cmsems:985

Ordering information: This working paper can be ordered from
fwalker@kellogg.northwestern.edu

Access Statistics for this paper

More papers in Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014. Contact information at EDIRC.
Bibliographic data for series maintained by Fran Walker (fwalker@kellogg.northwestern.edu this e-mail address is bad, please contact repec@repec.org).